EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
Author: Ross
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Textbook Question
Chapter 2, Problem 2.5TE
For any sequence of
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17.
Which of the following statements are not correct?
A. A discrete random variable X can assume only a finite number of possible values.
B. A discrete random variable X is any random variable whose possible values either constitute a
finite set or else can be listed in an infinite sequence in which there is a first element, a second
element, and son on.
C. A random variable X is said to be continuous if its set of possible values consists of an entire
interval on the number line.
D. Number of students in your statistics class is an example of a discrete random variable.
Prob-3
Pressurized air are being used in a manufacturing company in its daily operation. There are three compressors in service; two-screw type
compressors, (S1,S2) and one-reciprocal type compressor, (R). Each compressor, at any given time, is either off (0), or on (1). Assume that event A
is denoted to reciprocal compressor (R) that is always off. Event B is denoted that at least one of the screw type of compressor is always on. If
P(A)=41%; P(AUB)=97%, and at any given time, "probability of all compressor off'is 2%, compute probability of B; P(B) =?
Sol:
3. If {An, n ≥ 1) is an independent sequence of events, show
P(An) = P(A₂).
n=1
n=1
Chapter 2 Solutions
EBK FIRST COURSE IN PROBABILITY, A
Ch. 2 - A box contains 3 marbles: 1 red, 1 green, and 1...Ch. 2 - In an experiment, die is rolled continually until...Ch. 2 - Two dice are thrown. Let E be the event that the...Ch. 2 - A, B, and C take turns flipping a coin. The first...Ch. 2 - A system is composed of 5 components, each of...Ch. 2 - A hospital administrator codes incoming patients...Ch. 2 - Consider an experiment that consists of...Ch. 2 - Suppose that A and B are mutually exclusive events...Ch. 2 - A retail establishment accepts either the American...Ch. 2 - Sixty percent of the students at a certain school...
Ch. 2 - A total of 28 percent of American males smoke...Ch. 2 - An elementary school is offering 3 language...Ch. 2 - A certain town with a population of 100.000 has 3...Ch. 2 - The following data were given in a study of a...Ch. 2 - If it is assumed that all (525) poker hands are...Ch. 2 - Poker dice is played by simultaneously rolling 5...Ch. 2 - Twenty five people, consisting of 15 women and 10...Ch. 2 - Two cards are randomly selected from an ordinary...Ch. 2 - Two symmetric dice have had two of their sides...Ch. 2 - Suppose that you are playing blackjack against a...Ch. 2 - A small community organization consists of 20...Ch. 2 - Consider the following technique for shuffling a...Ch. 2 - A pair of fair dice is rolled. What is the...Ch. 2 - It two dice are rolled, what is the probability...Ch. 2 - A pair of dice is rolled until a sum of either 5...Ch. 2 - The game of craps is played as follows: A player...Ch. 2 - An urn contains 3 red and 7 black balls. Players A...Ch. 2 - An urn contains 5 red, 6 blue, and 8 green balls....Ch. 2 - An urn contains n white and m black balls, where n...Ch. 2 - The chess clubs of two schools consist of,...Ch. 2 - A 3-person basketball team consists of a guard, a...Ch. 2 - A group of individuals containing b boys and g...Ch. 2 - A forest contains 20 elk, of which 5 are captured,...Ch. 2 - The second Earl of Yarborough is reported to have...Ch. 2 - Seven balls are randomly withdrawn from an urn...Ch. 2 - Two cards are chosen at random from a deck of 52...Ch. 2 - An instructor gives her class a set of 10 problems...Ch. 2 - There are n socks. 3 of which are red, in a...Ch. 2 - There are 5 hotels in a certain town. If 3 people...Ch. 2 - If 4 balls are randomly chosen from an urn...Ch. 2 - If a die is rolled 4 times, what is the...Ch. 2 - Two dice are thrown n times in succession. Compute...Ch. 2 - a. If N people, including A and B, are randomly...Ch. 2 - Five people, designated as A, B, C, D, E, are...Ch. 2 - A woman has n keys, of which one will open her...Ch. 2 - How many people have to be in a room in order that...Ch. 2 - Suppose that 5 of the numbers 1, 2,..., 14 are...Ch. 2 - Given 20 people, what is the probability that...Ch. 2 - A group of 6 men and 6 women is randomly divided...Ch. 2 - In a hand of bridge, find the probability that you...Ch. 2 - Suppose that n balls are randomly distributed into...Ch. 2 - A closet contains 10 pairs of shoes. If 8 shoes...Ch. 2 - If 8 people, consisting of 4 couples, are randomly...Ch. 2 - Compute the probability that a bridge hand is void...Ch. 2 - Compute the probability that a hand of 13 cards...Ch. 2 - Two players play the following game: Player A...Ch. 2 - Prove the following relations: EFEEFCh. 2 - Prove the following relations: If EF, then FCEC.Ch. 2 - Prove the following relations: 3. F=FEFEC and...Ch. 2 - Prove the following relations: (1Ei)F=1EiF and...Ch. 2 - For any sequence of events E1,E2,..., define a new...Ch. 2 - Let E, F, and C be three events. Find expressions...Ch. 2 - Use Venn diagrams a. to simplify the expression...Ch. 2 - Prob. 2.8TECh. 2 - Suppose that an experiment is performed n times...Ch. 2 - Prove...Ch. 2 - If P(E)=.9 and P(F)=.8, show that P(EF).7. In...Ch. 2 - Show that the probability that exactly one of the...Ch. 2 - Prove that P(EF)=P(E)P(EF).Ch. 2 - Prove Proposition 4.4 by mathematical induction.Ch. 2 - An urn contains M white and N black balls. If a...Ch. 2 - Use induction to generalize Bonferronis inequality...Ch. 2 - Consider the matching problem. Example 5m, and...Ch. 2 - Let fn, denote the number of ways of tossing a...Ch. 2 - An urn contains n red and m blue balls. They are...Ch. 2 - Consider an experiment whose sample space consists...Ch. 2 - Consider Example 50, which is concerned with the...Ch. 2 - A cafeteria offers a three-course meal consisting...Ch. 2 - A customer visiting the suit department of a...Ch. 2 - A deck of cards is dealt out. What is the...Ch. 2 - Let A denote the event that the midtown...Ch. 2 - An ordinary deck of 52 cards is shuffled. What is...Ch. 2 - Urn A contains 3 red and 3 black balls, whereas...Ch. 2 - In a state lottery, a player must choose 8 of the...Ch. 2 - From a group of 3 first-year students, 4...Ch. 2 - For a finite set A, let N(A) denote the number of...Ch. 2 - Consider an experiment that consists of 6 horses,...Ch. 2 - A 5-card hand is dealt from a well-shuffled deck...Ch. 2 - A basketball team consists of 6 frontcourt and 4...Ch. 2 - Suppose that a person chooses a letter at random...Ch. 2 - Prove Booles inequality P(i=1Ai)i=1P(Ai)Ch. 2 - Show that if P(Ai)=1 for all i1, then P(i=1Ai)=1.Ch. 2 - Let Tk(n) denote the number of partitions of the...Ch. 2 - Five balls are randomly chosen, without...Ch. 2 - Four red, 8 blue, and 5 green balls are randomly...Ch. 2 - Ten cards are randomly chosen from a deck of 52...Ch. 2 - Balls are randomly removed from an urn initially...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Similar questions
- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.arrow_forwardThe conditional probability of E given that F occur is P(EF)= _____________. So in rolling a die the conditional probability of the event E. “getting a six,” given that the event F, “getting an even number.” has occurred is P(EF)= ____________.arrow_forwardAssume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.arrow_forward
- Let E and F be events in a sample space S. aThe probability of E and F occurring is P(EF)=______________. bIf the occurrence of E does not affect the probability of the occurrence F, then the events are called ____________. So in tossing a coin twice, the event E, getting heads on the first toss, and the event F, getting heads on the second toss, are ____________. cIf E and F are independent events, then the probability of E and F is P(EF)=________.arrow_forwardLet R be the set of all infinite sequences of real numbers, with the operations u+v=(u1,u2,u3,......)+(v1,v2,v3,......)=(u1+v1,u2+v2,u3+v3,.....) and cu=c(u1,u2,u3,......)=(cu1,cu2,cu3,......). Determine whether R is a vector space. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.arrow_forwardProve the Bonferroni inequalities, which state that for any events {A1, A2, ..., An} CF and any integer ke {1, 2,..., n}, k Pr(U²₁_₁A₁) ≤ Σ(-1)²-1 l=1 k Pr(U²1 Aj) ≥ Σ(−1)²-1 l=1 Σ SC1,2,...,n|| St Pr(Njës A;)if k is odd Σ Pr(njes Aj), if k is even SC1,2,...,n||S|=larrow_forward
- 3.17 Theorem Let {sn} be a sequence of real numbers. Let E and s* have the same meaning as in Definition 3. 16. Then s* has the following two properties: (a) s* e E. (b) If x> s*, there is an integer N such that n � N implies sn < x. Moreover, s* is the only number with the properties (a) and (b). Of course, an analogous result is true for s * . Proof (a) If s* = + 00, then E is not bounded above; hence {sn} is not bounded above, and there is a subsequence {snk } such that snk ) + 00. If s* is real, then E is bounded above, and at least one subsequential limit exists, so that (a) follows from Theorems 3.7 and 2.28. If s* = - 00, then E contains only one element, namely - 00, and there is no subsequential limit. Hence, for any real M, Sn > M for at most a finite number of values of n, so that Sn ) - 00. This establishes (a) in all cases. (b) Suppose there is a number x> s* such that Sn � x for infinitely many values of n. In that case, there is a number y E E such that y � x…arrow_forwardA “random digit" is a number chosen at random from {0, 1, ... ,9}, each with equal probability. A statistician choses n random digits. (a) For k = 0,1, ... , 9, let A be the event that all the digits are k or smaller. What is the probability of A, as a function of k and n? (b) Let B be the event that the largest digit chosen is equal to k. What is the probability of B1? Justify your answer carefully.arrow_forwardSolve itarrow_forward
- Suppose that A and B are events such that P (A|B) = P (B|A), P(AUB) = 1, and P(An B) > 0. Prove that P (A) >.arrow_forward(a) For each one of the statements below say whether the statement is true or false, explaining your answer. i. Let A and B be two events such that P(A) > 0 and P(B) > 0. If it holds that P(A|B) = 0, then P(B|A) = 1. 4 i. For two independent events A and B such that P(A) > 0) and P(B) > 0, then: P(AUB) = P(A) = P(B). iii. For a random variable X, then: Var(X)> Var(X + 2). iv. A random sample of size n is a sequence of n independent and non-identically distributed random variables. v. The standard normal distribution has fatter tails than the Student's t distribution with finite degrees of freedom. istribution witharrow_forward5arrow_forward
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